In the design of microwave amplifiers, lumped element networks are often required to obtain an impedance match between the source and the load or to improve the bandwidth of the circuit. The realization of lumped element networks on monolithic microwave integrated circuits (MMICs) is often accomplished with capacitors and spiral inductors. However, the use of spiral inductors presents certain significant limitations. For example, spiral inductors require large amounts of substrate area and air bridges, and for higher inductance values, the amount of substrate area increases further. Additionally, spiral inductors have limited bandwidths, high series resistance, cross-talk problems, and are quite difficult to model accurately. These limitations in the use of spiral inductors have provided a motivation to replace spiral inductors with active circuits capable of realizing inductance.
Inductance has been synthesized extensively with active devices in the audio frequency range with the use of generalized immittance converters (GICs), which are readily realized with operational amplifiers or operational transconductance amplifiers. Additionally, active shunt peaking to increase the bandwidth of VHF amplifiers has been accomplished by exploiting the inductive output impedance of a common collector transistor, as described in J. Choma, and A. E. Cosand, "A Broad-Banded Integrated Common-Collector Common-Base Differential Quartet", IEEE Journal of Solid-State Circuits, SC-16, No. 2, pp. 86-93 (April 1981). However, at microwave frequencies these circuits cannot be used, and other methods of simulating inductance must be employed.
Another active circuit which has been utilized to simulate inductance is the gyrator. A gyrator is a non-reciprocal two-port network which presents an impedance at one port proportional to the reciprocal of the impedance attached to a second port. In other words, a gyrator is basically an impedance inverter, where the load on the output is the inverse of the impedance on the input. A gyrator can simulate an inductance when a capacitor is connected to the second port, and as such is useful for active filter networks. FIG. 1a illustrates an ideal circuit model 10 of a gyrator, which includes a first voltage controlled current source 12 and a second voltage controlled current source 14. Circuit 10 realizes gyrator action since current source 12 is oriented such that current enters the common node 16, while current source 14 is oriented such that current leaves the common node 16. When the ideal gyrator circuit 10 is loaded with a capacitor 18 as illustrated in FIG. 1b, the input impedance looking into port 1 is given by the equation: ##EQU1## and the circuit 10 simulates a grounded inductor having a value of L=C/g.sup.2. As with the active devices discussed above, however, the use of gyrator circuits in amplifiers in the microwave frequency range has not been successfully accomplished.
Microwave frequency active inductor circuits have been reported which utilize GaAs field effect transistors (FETs), as described in Hara et al., "Broad-Band Monolithic Microwave Active Inductor and Its Application to Miniaturized Wide-Band Amplifiers", IEEE Transactions on Microwave Theory and Techniques, MTT-36, No. 12, pp. 1920-24 (Dec. 1988); and Hara et al., "Lossless Broad-Band Monolithic Microwave Active Inductors", IEEE Transactions on Microwave Theory and Techniques, MTT-37, No. 12, pp. 1979-84 (Dec. 1989). In the first of these publications, the circuit uses a common source-common gate FET cascode and a feedback resistor to produce inductance in the microwave frequency range. The inductance value is set by the feedback resistor and the series resistance of the realized inductor is approximately equal to 1/g.sub.m. In the second Hara et al. publication, the circuit employs a FET in a negative resistance configuration as the feedback element. The inductance realized by the second Hara et al. circuit is not as independent of frequency as the previous Hara et al. design, and the possibility of the circuit becoming unstable is significant.
An important aspect of the circuits in both Hara et al. publications is that the two FETs must be matched so that their intrinsic capacitances will cancel each other out. If this were not the case, a flat inductive response in the microwave frequency region would not be possible. Thus, in all cases, for the Hara et al. circuits to be broadband and realize a flat inductive response, the FETs must be identical and under the same bias.